Question
Answer
$$\dfrac{\dfrac{1}{2\sqrt{462}-20}}{63}=\dfrac{\dfrac{\sqrt{462}+10}{724}}{63}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{1}{2\sqrt{462}-20}}{63}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{1}{2\sqrt{462}-20}\frac{2\sqrt{462}+20}{2\sqrt{462}+20}}{63} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\frac{2\sqrt{462}+20}{1848+40\sqrt{462}-40\sqrt{462}-400}}{63} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\frac{2\sqrt{462}+20}{1448}}{63} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{\frac{\sqrt{462}+10}{724}}{63}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 2 \sqrt{462} + 20} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 1 } \cdot \left( 2 \sqrt{462} + 20\right) = \color{blue}{1} \cdot 2 \sqrt{462}+\color{blue}{1} \cdot20 = \\ = 2 \sqrt{462} + 20 $$ Simplify denominator. $$ \color{blue}{ \left( 2 \sqrt{462}-20\right) } \cdot \left( 2 \sqrt{462} + 20\right) = \color{blue}{ 2 \sqrt{462}} \cdot 2 \sqrt{462}+\color{blue}{ 2 \sqrt{462}} \cdot20\color{blue}{-20} \cdot 2 \sqrt{462}\color{blue}{-20} \cdot20 = \\ = 1848 + 40 \sqrt{462}- 40 \sqrt{462}-400 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 2. |
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